Christian Volk

Probing relaxation times in graphene quantum dots

Graphene quantum dots are attractive candidates for solid-state quantum bits. In fact, the predicted weak spin-orbit and hyperfine interaction promise spin qubits with long coherence times. Graphene quantum dots have been extensively investigated with respect to their excitation spectrum, spin-filling sequence and electron-hole crossover. However, their relaxation dynamics remain largely unexplored. This is mainly due to challenges in device fabrication, in particular concerning the control of carrier confinement and the tunability of the tunnelling barriers, both crucial to experimentally investigate decoherence times. Here we report pulsed-gate transient current spectroscopy and relaxation time measurements of excited states in graphene quantum dots. This is achieved by an advanced device design that allows to individually tune the tunnelling barriers down to the low megahertz regime, while monitoring their asymmetry. Measuring transient currents through electronic excited states, we estimate a lower bound for charge relaxation times on the order of 60–100 ns.

Disorder induced Coulomb gaps in graphene constrictions with different aspect ratios

We present electron transport measurements on lithographically defined and etched graphene nanoconstrictions with different aspect ratios including different lengths (l) and widths (w). A roughly length-independent disorder induced effective energy gap can be observed around the charge neutrality point. This energy gap scales inversely with the width even in regimes where the length of the constriction is smaller than its width (l<w). In very short constrictions, we observe both resonances due to localized states or charged islands and an elevated overall conductance level (0.1−1e2/h), which is strongly length-dependent in the gap region. This makes very short graphene constrictions interesting for highly transparent graphene tunneling barriers.

Etched graphene quantum dots on hexagonal boron nitride

We report on the fabrication and characterization of etched graphene quantum dots (QDs) on hexagonal boron nitride (hBN) and SiO2 with different island diameters. We perform a statistical analysis of Coulomb peak spacings over a wide energy range. For graphene QDs on hBN, the standard deviation of the normalized peak spacing distribution decreases with increasing QD diameter, whereas for QDs on SiO2 no diameter dependency is observed. In addition, QDs on hBN are more stable under the influence of perpendicular magnetic fields up to 9 T. Both results indicate a substantially reduced substrate induced disorder potential in graphene QDs on hBN.

Charge detection in a bilayer graphene quantum dot

We show measurements on a bilayer graphene quantum dot with an integrated charge detector. The focus lies on enabling charge detection with a 30 nm wide bilayer graphene nanoribbon located approximately 35 nm next to a bilayer graphene quantum dot with an island diameter of about 100 nm. Local resonances in the nanoribbon can be successfully used to detect individual charging events in the dot even in regimes where the quantum dot Coulomb peaks cannot be measured by conventional techniques.

Graphene-based charge sensors.

We discuss graphene nanoribbon-based charge sensors and focus on their functionality in the presence of external magnetic fields and high frequency pulses applied to a nearby gate electrode. The charge detectors work well with in-plane magnetic fields of up to 7 T and pulse frequencies of up to 20 MHz. By analyzing the step height in the charge detectors current at individual charging events in a nearby quantum dot, we determine the ideal operation conditions with respect to the applied charge detector bias. Average charge sensitivities of 1.3 × 10(-3)e Hz(-1/2) can be achieved. Additionally, we investigate the back action of the charge detector current on the quantum transport through a nearby quantum dot. By varying the charge detector bias from 0 to 4.5 mV, we can increase the Coulomb peak currents measured at the quantum dot by a factor of around 400. Furthermore, we can completely lift the Coulomb blockade in the quantum dot.

Fabrication of coupled graphene–nanotube quantum devices

We report on the fabrication and characterization of all-carbon hybrid quantum devices based on graphene and single-walled carbon nanotubes. We discuss both carbon nanotube quantum dot devices with graphene charge detectors and nanotube quantum dots with graphene leads. The devices are fabricated by chemical vapor deposition growth of carbon nanotubes and subsequent structuring of mechanically exfoliated graphene. We study the detection of individual charging events in the carbon nanotube quantum dot by a nearby graphene nanoribbon and show that they lead to changes of up to 20% of the conductance maxima in the graphene nanoribbon, acting as a well performing charge detector. Moreover, we discuss an electrically coupled graphene-nanotube junction, which exhibits a tunneling barrier with tunneling rates in the low GHz regime. This allows us to observe Coulomb blockade on a carbon nanotube quantum dot with graphene source and drain leads.

Electronic Excited States in Bilayer Graphene Double Quantum Dots

We report tunneling spectroscopy experiments on a bilayer graphene double quantum dot device that can be tuned by all-graphene lateral gates. The diameter of the two quantum dots are around 50 nm and the constrictions acting as tunneling barriers are 30 nm in width. The double quantum dot features additional energies on the order of 20 meV. Charge stability diagrams allow us to study the tunable interdot coupling energy as well as the spectrum of the electronic excited states on a number of individual triple points over a large energy range. The obtained constant level spacing of 1.75 meV over a wide energy range is in good agreement with the expected single-particle energy spacing in bilayer graphene quantum dots. Finally, we investigate the evolution of the electronic excited states in a parallel magnetic field.

Reducing disorder in graphene nanoribbons by chemical edge modification

We present electronic transport measurements on etched graphene nanoribbons on silicon dioxide before and after a short hydrofluoric acid (HF) treatment. We report on changes in the transport properties, in particular, in terms of a decreasing transport gap and a reduced doping level after HF dipping. Interestingly, the effective energy gap is nearly unaffected by the HF treatment. Additional measurements on a graphene nanoribbon with lateral graphene gates support strong indications that the HF significantly modifies the edges of the investigated nanoribbons leading to a significantly reduced disorder potential in these graphene nanostructures.

Etched graphene single electron transistors on hexagonal boron nitride in high magnetic fields

We report on the fabrication and electrical characterization of etched graphene single electron transistors (SETs) of various sizes on hexagonal boron nitride (hBN) in high magnetic fields. The electronic transport measurements show a slight improvement compared to graphene SETs on SiO2. In particular, SETs on hBN are more stable under the influence of perpendicular magnetic fields up to 9 T in contrast to measurements reported on SETs on SiO2. This result indicates a reduced surface disorder potential in SETs on hBN, which might be an important step toward clean and more controllable graphene quantum dots (QDs).

Tunable capacitive inter‐dot coupling in a bilayer graphene double quantum dot

We report on a double quantum dot which is formed in a width-modulated etched bilayer graphene nanoribbon. A number of lateral graphene gates enable us to tune the quantum dot energy levels and the tunneling barriers of the device over a wide energy range. Charge stability diagrams and in particular individual triple point pairs allow to study the tunable capacitive inter-dot coupling energy as well as the spectrum of the electronic excited states on a number of individual triple points. We extract a mutual capacitive inter-dot coupling in the range of 2–6 meV and an inter-dot tunnel coupling on the order of 1.5 µeV. (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)